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Question -

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charged and the cost of food per day. [CBSE 2000]



Answer -

Let the fixed charge of the college hostel = ₹ x
and daily charges = ₹ y
According to the given conditions,
x + 20y = 1000 …(i)
x + 26y =1180 …(ii)
Subtracting (i) from (ii), we get
6y = 180
=> y = 30
Substituting the value of y in (i)
x + 20 x 30 = 1000
=> x + 600 = 1000
=> x = 1000 – 600 = 400
Fixed charges = ₹ 400 and daily charges = ₹ 30

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